MinT - Best Known (187−47, 187, s)-Nets in Base 3

Best Known (187−47, 187, s)-Nets in Base 3

(187−47, 187, 288)-Net over F₃ — Constructive and digital

Digital (140, 187, 288)-net over F₃, using

t-expansion [i] based on digital (139, 187, 288)-net over F₃, using
- 5 times m-reduction [i] based on digital (139, 192, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 64, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(187−47, 187, 788)-Net over F₃ — Digital

Digital (140, 187, 788)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−47, 187, 34009)-Net in Base 3 — Upper bound on s

There is no (140, 187, 34010)-net in base 3, because

1 times m-reduction [i] would yield (140, 186, 34010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55558 724868 762306 768278 745812 496976 768709 715892 855337 003097 176919 642855 220661 641464 513897 > 3¹⁸⁶ [i]